Digital Library of Mathematical Functions
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16 Generalized Hypergeometric Functions and Meijer G-FunctionGeneralized Hypergeometric Functions

§16.9 Zeros

Assume that p=q and none of the aj is a nonpositive integer. Then Fpp(a;b;z) has at most finitely many zeros if and only if the aj can be re-indexed for j=1,,p in such a way that aj-bj is a nonnegative integer.

Next, assume that p=q and that the aj and the quotients (a)j/(b)j are all real. Then Fpp(a;b;z) has at most finitely many real zeros.

These results are proved in Ki and Kim (2000). For further information on zeros see Hille (1929).